The so-called Australian "birthers", a nod to similar US right-wing attacks against President Barack Obama, have been claiming in blogs and on social media for months that Mr Abbott, who was born in London but emigrated to Australia as a child, is a dual citizen.

Labor MP Tim Watts has urged supporters to focus on the government's policies rather than spread a false smear campaign. Photo: Alex Ellinghausen

Mr Abbott's office has rejected the claims, saying the Prime Minister is an Australian citizen and denies he holds dual citizenship. Those making the claims have called on Mr Abbott to produce documents to prove he renounced his British citizenship before becoming an MP in 1994.

He was immediately attacked by Twitter users who said Mr Abbott could shut down the conspiracy theories by publishing documents proving he had renounced his British citizenship. Mr Watts replied "well it didn't resolve it for Obama. The solution here is promoting respect for democratic processes and results".

The conspiracy theory has been largely ignored by the mainstream media although recently it has gained some coverage.

Mr Watts told Fairfax Media: "I'd say to people of the left, attack Tony Abbott because of the terrible job he is doing, but don't attack his political legitimacy."

"I can understand people's anger, we are fighting over issues that are important but let's keep the focus on those issues and not questioning the process itself," he said. "If you care about our democracy, focus on substance and not the perceived legitimacy of our opponents."

He said trying to bring down a government on the grounds of legitimacy, rather than after a battle on policy was nothing more than an "attempt to subvert the democratic process by waving a magic wand".

Mr Watts said he was "alarmed" by the "unfortunate trend" in politics of questioning an opponent's "legitimacy" and said Mr Abbott needed to bear some blame.

"It's no longer enough to say your political opponent is wrong, people now take the next step and say they're illegitimate," he said.

"Tony Abbott does bear some responsibility for his attacks on the previous government for calling it illegitimate."

Mr Abbott targeted Labor's slim majority in the lower house during its last spell in office and not Ms Gillard's birth-rite but Mr Watts said there was no difference.

"It's important that anyone who wants to change Australian society through the democratic process defends that process," Mr Watts said.